The stepchildren thing is a red herring - what i mean by that is that you should neither feel guilty about being protective with your pfb nor should you feel guilty for 'not trusting' your stepchildren.
Your stepchildren need to bond with your baby. This includes the eldest being allowed to pick him up and your youngest being able to hold him.
But....this should generally be done under supervision so that the seven year old holds the baby's head correctly and the youngest is sat nicely with arms out for you to give baby to cuddle and make sure does not drop. The older one cannot do that for the younger - too much responsibility.
If all three are in the same room then yes, theoretically they can all be together/coo together provided that the baby is safe tied into a baby bouncer or in a bassinet or in a travel cot or on a playmat/in a playpen.
Ground rules to be established
if baby asleep they both let him sleep
if baby in a playpen or on a playmat the youngest does not decide to leap into playpen or stand up suddenly/dance around the playmat
if baby having cuddle with the oldest youngest can stroke but not try to take and oldest does not try to get up and move with - certainly not at the age you are talking
if baby in basket youngest not to swing it without adult present
if baby in travel cot other two to distract with soft toys only, nothing too heavy
Yes they can be left alone for 5-10 mins but 15 too long unless baby asleep somewhere safe
why i think this
because I have had similar age gaps and you are right in thinking the eldest may be clumsy and the youngest may be rough. You would think that once you were onto your second let alone third which is why the stepchildren part is a misnomer. Your husband's ex was probably just as protective over her second when her four year old wanted to play with the newborn - your partner has either forgotten that or the four year old was amazingly diligent.
So - my seven year old could carry and cuddle but could not lift sister from the playmat - dropped her at eleven weeks
my three year old could not let her brother sleep - would poke tickle and pinch awake
neither could dance near the playmat - had a tendency to fall onto it we are very clumsy in my family
my three year old would swing a moses basket too high too quickly
both would drop plastic rattles on baby's head
my three year old would jump into the playpen and near kick baby in the head
what they could do
both could cuddle and soothe baby in their arms brilliantly once positioned safely
eldest could carry younger ones in an ergo
eldest could push prams and pushchairs
youngest could play alongside me with baby on the playmat or in the playpen
both could sing twinkle incy or pat a cake
both could lay on a bed with baby in the middle for group hug
both could fetch nappies wipes cream etc for me
I did have to bodyguard baby from three year old as it was treated like a doll and with jealousy involved was sometimes poked. Rough play is/was normal but certain behaviours like pinching biting not okay.
All have to feel like family as they ARE family but this can be managed in a good way with lots of praise doing the above and following those ground rules - the eldest will understand as would feel awful if did drop the baby trying to lift her. But they do need to feel involved.
But once established it should be that the baby can lay in carrycot for example whilst you grab a brew, nip in shower, go to the loo
Then both kids get a biccy, lots of praise - how proud you are, how lucky the baby is to have such a good big sister/brother etc
In three years time the eldest at ten will be a Godsend - can help with spoonfeeding burping etc- and the younger at six will be similar to the older one now. If you have a second baby you will then be guarding said baby from your current pfb at three 
Last thing - it is normal to be protective and feel 'mine mine mine'
whether baby is with siblings, inlaws, friends or childcarers but you will learn to let go and it is good for your pfb to have lots of interaction.
Secondly your baby is going to fall, be dropped or have an accident of some kind. It will happen either on your watch or with dp or siblings or whilst you are there and you will cry and feel guilty and possibly snap or recriminate but your baby will be fine. They are luckily very very sturdy.
Finally if your partner is arguing because he feels his children are perfectly capable of being with his third child without breaking him please be gentle - he is protecting his pfb in the same way. Which makes him a Keeper.
